Problem: A circle with area $36\pi$ has a sector with a $16^\circ$ central angle. What is the area of the sector? ${36\pi}$ $\color{#9D38BD}{16^\circ}$ ${\dfrac{8}{5}\pi}$
Answer: The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{16^\circ}{360^\circ} = \dfrac{A_s}{36\pi}$ $\dfrac{2}{45} = \dfrac{A_s}{36\pi}$ $\dfrac{2}{45} \times 36\pi = A_s$ $\dfrac{8}{5}\pi = A_s$